Freeform surfaces play an increasingly important role in contemporary
architecture. While digital models are easily created, the actual
fabrication and construction of architectural freeform structures remains a
challenge. In order to make a freeform design realizable, an optimization
process known as rationalization has to be applied. This means its
decomposition into smaller parts, thereby meeting two competing objectives:
feasibility, and consistency with the designer’s intentions. Depending on
what constitutes the design, there have been different approaches to this
problem (with strong involvement of our research group) which have led to
different kinds of specific geometric and computational questions. Mostly
these questions involve replacing smooth surfaces (possibly with an
additional curve network on them) by other structures like meshes with
special properties. The guiding thought in all considerations is the
efficient manufacturing of the surface parts and their respective necessary
supporting/connecting elements. Both simple geometry and repetition of
elements contribute to this goal of efficiency. In any case, a rationalized
design is the output of a possibly very complicated nonlinear optimization,
and it is very hard to make changes to such a highly constrained geometric
model.

The present project developed methodology for unifying two traditionally
separate phases in freeform architecture, namely (i) shape design and (ii)
rationalization in view of the actual fabrication. While motivated by
architecture, such fabrication-aware design or design exploration makes
sense in many other applications as well.

The applied method is shape space exploration. This means that we view the
set of all feasible designs which fulfil the constraints (posed by
manufacturing and other practical aspects) as points of a high-dimensional
manifold (shape space). Then design exploration is accomplished by an
efficient navigation in this manifold. The ideas come from computational
differential geometry and nonlinear optimization. We developed efficient
algorithms for interactive modelling while satisfying constraints from
manufacturing and in the case of architecture also from statics. Besides
Architecture, we mainly studied modelling of so-called developable surfaces
since they play an important role in several manufacturing technologies and
their treatment in CAD systems has so far been quite limited.